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Diffusion of autowaves. Evolution equation for slowly varying autowaves. (English) Zbl 0683.76072
Summary: An evolution equation is developed for the phase of a nearly periodic and nearly plane autowave in the general reaction-diffusion system. It is shown that the evolution depends on three major processes: dispersion, lateral diffusion, accounting for the dependence of the velocity on the front curvature, and longitudinal diffusion, responsible for aligning the wavevector in the direction of its propagation. The evolution equation includes many related well-known equations as special cases.

MSC:
76R50 Diffusion
35K57 Reaction-diffusion equations
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